Coures Outline and Syllabus

This course is an introduction to nonlinear dynamics with applications to biology targeted to junior/senior engineering students and 1st year graduate students in engineering and quantitative life sciences.

Questions for Professor Rickus or TA Mike

9/7/07

Q: I was wondering how to show that the origin is stable in a super critical pitchfork with r=0 since the slope test fails. Also, what is the stability at the origin when r=0 for the subcritical pitchfork case and by what reasoning?

A: When the linear stability analysis (slope test) fails, the way to determine the stability definitively is to look at the phase portrait. Plot dx/dt versus x for that value of your parameter, r. Is the fixed point of interest stable or unstable? You should be able to tell by the direction of the vector fields on either side of the fixed point. Try this yourself for the supercritical and subcritical and see what you get. After doing this. See me if you are still confused.

How Purdue students can get a copy of Mathematica Students may purchase an annual "student edition" license by visiting the BoilerCopyMaker facility on the main floor of the Purdue Memorial Union. The cost is $45 per license (multiple licenses may be purchased - e.g., one each for a desktop and laptop or one for use on your Windows computer and another for your Linux system). These licenses expire at the end of each academic year (in mid-late August). The fee is not pro rated.

XPPAUT
XPP/AUTO is designed to solve differential equations with an emphasis on a phase plane and bifurcation graphing. You may find this useful for creating particularly hairly bifurcation diagrams.
the software can be downloaded from here

Background Math to Brush Up On

these following things should be 2nd nature to you. if they are hazing from the summer fun, it would be best to brush up now.